Time dependent density functional theory calculation of van der Waals coefficient C6_{6} of alkali-metal atoms Li, Na, K, alkali dimers Li2_{2}, Na2_{2}, K2_{2} and sodium clusters Nan_{n}

In this paper we employ all-electron time dependent density functional theory (TDDFT) to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) $C_{6}$ of alkali-metal atoms Li, Na, K, alkali-metal atom dimers Li$_{2}$, Na$_{2}$, K$_{2}$ and sodium clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder expression which relates it to the frequency dependent linear polarizabilty at imaginary frequencies. The frequency dependent polarizabilities are calculated by employing TDDFT--based complete sum-over-states expressions for the atoms, and direct TDDFT linear response theory for the closed shell dimers and clusters.Comment: 14 pages of text and 4 figure

Velocity dispersion due to anelasticity; implications for seismology and mantle composition

The concept of a relaxation spectrum is used to compute the absorption and dispersion of a linear anelastic solid. The Boltzmann after-effect equation is solved for a solid having a linear relationship between stress and strain and their first time derivatives, the ‘standard linear solid’, and having a distribution of relaxation times. The distribution function is chosen to give a nearly constant Q over the seismic frequency range. Both discrete and continuous relaxation spectra are considered. The resulting linear solid has a broad absorption band which can be interpreted in terms of a superposition of absorption peaks of individual relaxation mechanisms. The accompanying phase and group velocity dispersion imply that one cannot directly compare body wave, surface wave, and free oscillation data or laboratory and seismic data without correcting for absorption. The necessary formalism for making these corrections is given. In the constant Q regions the correction is the same as that implied in the theories of Futterman, Lomnitz, Strick and Kolsky

Time-Domain Learned Digital Back-Propagation

Performance for optical fibre transmissions can be improved by digitally reversing the channel environment. When this is achieved by simulating short segment by separating the chromatic dispersion and Kerr nonlinearity, this is known as digital back-propagation (DBP). Time-domain DBP has the potential to decrease the complexity with respect to frequency domain algorithms. However, when using finer step in the algorithm, the accuracy of the individual smaller steps suffers. By adapting the chromatic dispersion filters of the individual steps to simulated or measured data this problem can be mitigated. Machine learning frameworks have enabled the gradient-descent style adaptation for large algorithms. This allows to adopt many dispersion filters to accurately represent the transmission in reverse. The proposed technique has been used in an experimental demonstration of learned time-domain DBP using a four channel 64-GBd dual-polarization 64-QAM signal transmission over a 10 span recirculating loop totalling 1014 km. The signal processing scheme consists of alternating finite impulse response filters with nonlinear phase shifts, where the filter coefficient were adapted using the experimental measurements. Performance gains to linear compensation in terms of signal-to-noise ratio improvements were comparable to those achieved with conventional frequency-domain DBP. Our experimental investigation shows the potential of digital signal processing techniques with learned parameters in improving the performance of high data rate long-haul optical fibre transmission systems

Equalization in Dispersion-Managed Systems Using Learned Digital Back-Propagation

In this paper, we investigate the use of the learned digital back-propagation (LDBP) for equalizing dual-polarization fiber-optic transmission in dispersion-managed (DM) links. LDBP is a deep neural network that optimizes the parameters of DBP using the stochastic gradient descent. We evaluate DBP and LDBP in a simulated WDM dual-polarization fiber transmission system operating at the bitrate of 256 Gbit/s per channel, with a dispersion map designed for a 2016 km link with 15% residual dispersion. Our results show that in single-channel transmission, LDBP achieves an effective signal-to-noise ratio improvement of 6.3 dB and 2.5 dB, respectively, over linear equalization and DBP. In WDM transmission, the corresponding $Q$-factor gains are 1.1 dB and 0.4 dB, respectively. Additionally, we conduct a complexity analysis, which reveals that a frequency-domain implementation of LDBP and DBP is more favorable in terms of complexity than the time-domain implementation. These findings demonstrate the effectiveness of LDBP in mitigating the nonlinear effects in DM fiber-optic transmission systems

Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points

We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. Based on an algorithmic idea by Henley, we simulate a stochastic process of classical dimer configurations in continuous time and perform a stochastic analytical continuation to obtain the dynamical correlations in momentum space and the frequency domain. This approach allows us to observe directly the dispersion relations and the evolution of the spectral intensity within the Brillouin zone beyond the single-mode approximation. On the square lattice, we confirm analytical predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0) and further reveal the existence of shadow bands close to the wavevector (0,0). On the cubic lattice the spectrum is also gapless but here only a single soft mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The soft mode has a quadratic dispersion at very long wavelength, but crosses over to a linear behavior very rapidly. We believe this to be the remnant of the linearly dispersing "photon" of the Coulomb phase. Finally the triangular lattice is in a fully gapped liquid phase where the bottom of the dimer spectrum exhibits a rich structure. At the M point the gap is minimal and the spectral response is dominated by a sharp quasiparticle peak. On the other hand, at the X point the spectral function is much broader. We sketch a possible explanation based on the crossing of the coherent dimer excitations into the two-vison continuum.Comment: 16 pages, 7 figures, published versio

Time scales of mesoscale variability and their relationship with space scales in the North Atlantic

A systematic study of characteristic time scales of mesoscale variability over the North Atlantic was done using two years of Geosat data. Time scales are first characterized by 10° latitude by 10° longitude bins. A more detailed description was obtained by globally mapping the Sea Level Anomaly temporal correlation after one cycle (17.05 days). The scales are shortest in areas of high mesoscale activity (Gulf Stream, North Atlantic Current) while relatively long time scales are observed over the Mid-Atlantic Ridge and in the eastern part of the basin. In general, time scales are not proportional to space scales. Propagation velocities obtained by dividing space scales by time scales appear to be minimal east of the Mid-Atlantic Ridge. Frequency-wavenumber spectral analysis complemented this statistical description of mesoscale variability. It shows that the dominant wavelengths of around 200 to 500 km (depending on latitude) are associated with long periods (\u3e150 days) in the eastern part of the basin, while near the Gulf Stream significant energy is found at shorter periods. Propagation velocities are generally westward. Pseudo-dispersion relations deduced from Geosat data suggest two distinct dynamic regimes, as in quasigeostrophic turbulence models: a turbulent regime for smaller scales, with proportionality between space and time scales, and an apparently more linear regime where an inverse dispersion relation is found in the eastern part of the basin. This latter characteristic is in agreement with quasigeostrophic models forced by fluctuating winds

Astrophysical Gyrokinetics: Basic Equations and Linear Theory

Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code {\tt GS2} in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.Comment: emulateapj, 24 pages, 10 figures, revised submission to ApJ: references added, typos corrected, reorganized and streamline

Spectrograms of ship wakes: identifying linear and nonlinear wave signals

A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. We use a simple weakly nonlinear theory to identify higher order effects in a spectrogram and, while the high speed ferry data is very noisy, we propose that certain additional features in the experimental data are caused by nonlinearity. Finally, we provide a possible explanation for a further discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceleration.Comment: 21 pages, 10 figures, submitte